If you could leave the earth and travel faster than the speed of light?

No. Time doesn't slow down for you, in your frame of reference, it remains normal, just as it does for the people you left behind in THEIR frame of reference. However, because of the need to conserve the speed of light as a constant, the difference arises when you compare the two frames of reference. While you would still be, say, six months older than when you left, the amount of time passed in the Earth's time frame would be considerably more and you would, effectively, have traveled into their future.

This is what I learned in a physics lecture.

Time= Distance/Speed

So imagine a clock keeping time by bouncing a ball up and down. say it bounces 5 cm every second. This is on earth, the standard measurement as a constant for relativity. Now imagine the same clock on a spaceship. The spaceship is moving at the speed of light. So every second, the clock travels up&down 5 cm, but ALSO travels forward 300 000 km/second with the space ship. So you can see that the factors are increased. This is why time passes slightly slower, even in today's orbiting spacecraft. They actually have to adjust gps clocks by 38 microseconds every day. This gets exponentially more significant when you hit light speed

Go the the perimeter institute site for more and clearer info

No it doesn't work like that and you can't travel faster than the speed of light according to the very theory of relativity that you are asking about. If you want to hypothetically travel faster than light you have to ignore special relativity.

Here's what happens to time:

t' = t/sqrt(1-v^2 / c^2)

now first why you can't go faster than light.

If v>c then v^2 > c^2 so 1-v^2/c^2 becomes negative and the square root of a negative number is imaginary. So we can't go faster than light (excpet of course in abstract mathematics and end up imagining exotic particles like tachions).

The Lorents transform we just discussed shows that regardless of the direction you're travelling the fastest rate you will see clocks move is when you're statitionary relative to the clock. Regardless of direction if you are moving towards or away from the clock the clock will appear to run slow.

In 1971 an experiemnt was done involving four atomic clocks and some aircraft traveling around the world in opposite directions. Here's the results of those experiments:

http://en.wikipedia.org/wiki/Hafele%E2%80%93Keatin...

It isn't leaving earth that does it - it is traveling fast, and you don't even have to got faster than the speed of light, just pretty fast - it is the acceleration and velocity - and to get back to earth you have to change direction (accelerate "sideways") and put as much energy into coming back as you did going out.

Our GPS satellites that are constantly being accelerated sideways by gravity have their atomic clocks slowed and the processors have to keep that in mind - they are not "aging" at the same rate as clocks kept here on earth.